Part of Francis Alÿs’s installation Fabiola. The Belgian artist spent 15 years collecting these images by a range of creators. Photograph: Ben Stansall/AFP/Getty Images

It would be hard to imagine a more startling show of portraits than the 300 heads now assembled, with barely an inch between them, in Fabiola at the National Portrait Gallery. The spectacle is overwhelming. It is not just the critical mass of so many faces, floor to ceiling, nor the fact that some of these works might not ordinarily be found in a public gallery. It is that they all show exactly the same woman.

The same woman, what is more, in exactly the same pose: facing right, her head in profile, hooded in a red veil against a dark background. That she is a cult figure is obvious, even to those who have no idea who she is; that the cult is religious becomes apparent from the veil. But beyond that, what strikes over and again is the paradoxical sense that no matter how alike these images are - how alike they aim to look - each is tellingly different.

Fabiola is a Catholic saint and follower of St Jerome, who wrote a beautiful eulogy of her virtues when she died in 399. Born into a patrician family in Rome, she was married twice - once to a brute, as Jerome implies, whom she committed the sin of divorcing, next to a man whose early death she grieved in the streets of Rome before renouncing the world for her faith.

Fabiola might have remained obscure had not Cardinal Wiseman, Archbishop of Westminster, written an improbably racy bestseller about her life in 1850 which was translated into 10 languages; and if the 19th-century French artist (who would himself be otherwise obscure) Jean-Jacques Henner had not painted his celebrated "portrait".

The first of the many tantalising questions raised by this show is just how Henner's portrait came to dominate all future images of the saint for the original disappeared long ago. It survives only in black-and-white reproductions based, one must suppose, either on a primitive photograph or an etching; and yet almost every artist here has painted the hair brown and the veil decisively red. It is as if Henner's painting, even at several removes, was unanimously upheld as the right version of Fabiola, quite a tribute to his imagination for he had no idea how she looked.

But creativity is the true subject of this show - art and its power, its uses. This is the reason, one feels, that Belgian artist Francis Alÿs has spent 15 years unearthing hundreds of images by a whole range of creators from skilled painters to mediocre hacks and thrift-shop amateurs. There are hyper-real Fabiolas and Fabiolas worked on linen and black velvet. There are wood carvings, embroideries and icons accoutred with actual veils. There are glass works, pastels and images on tin foil. There is even a Fabiola laboriously worked in varnished sesame seeds.

Alÿs, one of the most humane of contemporary artists, is a great co-ordinator of ideas and people. He once brought 500 citizens together to move a vast sand dune, transforming the landscape (and their view) and one of his most beguiling works traces the sundial effect of a flagpole in Mexico City, providing shadow for passers-by even as it measures the passing of their day. With Fabiola, he has turned the act of collecting into a prism for looking. Where did this image come from, why was it made and by what sort of mind? Each picture inflects questions about the next. Fabiola looks more or less western, Mexican, eastern European. She acquires green eyeshadow, turns bottle blonde, appears by turns serene, tragic, meek, compassionate, powerful. Each artist makes her again to him or herself.

One has given her a presence so immediate she might be posing before him; another has tried to return her to Rome with the look of a classical mosaic. The portrait may be a sign of the times - art deco, Forties Hollywood - or it might be an absolutely timeless act of pure devotion. As Alÿs observes, the one defining constant in all this multiplicity is actually the scrolling fold of her veil, which looks variously like a loop, hook or ear, depending on the artist's abilities.

Why they were painted - altarpiece, ex-voto, act of gratitude, penitence or prayer, just for the comfort of her company (Fabiola is the patron saint of the abused and widowed) - may speak of the artist's private need or devotion. But what this immense assembly of images conveys above all is the universal power of the portrait.

Portraits have powers quite other than pictures of apples or rolling fields; they appear to us as people first, however momentarily, before they revert to pictures. Fabiola is the purest expression of this effect: friend, heroine, living saint to all these people, she has services to perform in this world, not least in proving that there are an infinite number of ways to paint a portrait.